While our result is formulated for very general resource theories, we also focus on three specific examples: resource theory of athermality [1]}, [2]}, [3]}, entanglement theory [4]}, [5]}, [6]} and resource theory of coherence [7]}, [8]}, [9]}.
In each theory we show how our general results apply to these specific cases and we identify the relevant resource monotone to evaluate the resources needed to prepare the catalyst.
